T-shirt Design Contest - aka Polar Graphing Project

aka, Have I mentioned how much I love www.desmos.com?

I teach a Trigonometry/Precalculus class.  It is a regular level 4th year high school math class.  It comes after Algebra 2, and I like to think that it prepares at least some students for Calculus.  However, most of my students aren't going to ever take Calculus.  Very few of them are going to major in anything that would require advanced math.  At the same time, these are all wonderful kids, most of whom are choosing to take this class as their elective senior year, even though they don't need it.  I periodically remind them that it's an elective and that they chose to be here.  Because they're seniors.  For those of you who have ever taught seniors, or remember being a senior, it's the end of April.  Enough said?

So we worked hard all year.  At least some of the time I felt like they worked hard, too, so I'm using that "we" somewhat loosely.  And we got to a unit on Polar Coordinates.

What does someone who isn't going into math really need to know about Polar Coordinates?  Well, I think they should know it's a different system of graphing equations.  They should understand the idea of having two systems for the same purpose (Metric/English, degrees/radians).  Maybe they should know how to plot some graphs and analyze equations.  Definitely convert some ordered pairs from polar to rectangular and vice versa.  Maybe convert a few equations, too.

But I think the most important goal of this unit for me, was to get them to finally start seeing the beauty in Mathematics.  They are so used to doing stuff all the time, how often do we let them stand back and just admire how beautiful Math really is?  And once they had a chance to stand back, it was time to do stuff again, only the stuff they were doing was creating beautiful designs out of polar equations using www.desmos.com.  

I don't want to say anything bad about the TI graphing calculators.  Lord knows, I've had some good times with mine, starting back in 1996.  Back in 1996, it was the coolest techi-est toy I owned.  (My family emigrated to the US in '92, and video games were not part of the family budget.) But it's 2014.  And that screen is just about as pixelated as it was back then.  The new line has color, and it looks better, to be sure, but it's still not nearly as beautiful as desmos.  

So the project was simple.  Come up with your own beautiful design.  I gave almost no other directions.  Here's the assignment sheet.
I compiled the designs in each class and used a Google Form to have them vote on their favorite option (no names attached to the designs.)  
Here's the winning design from the first class: 

And the second class: 

And here's the design that desmos chose to post on their site, to the utter delight of the entire class.

Here are a couple TI designs, just for comparison.

So I guess I'm not sure if this project assesses any understanding of any learning targets, but it definitely helped my students see math in a different, more appreciative, way.  Now I need to find a place that might be able to print these onto t-shirts for very little $!